1. Field of the Invention
The present invention relates to a method for predicting the production of an underground reservoir by updating a geologic model constrained by production data and seismic data in time. The method is part of reservoir characterization, whose objective is to provide reliable images of reservoirs in order to better predict their behavior and to optimize their development scheme.
2. Description of the Prior Art
The following documents illustrate the state of the art and are discussed by their reference number in the description hereafter.    1. F. ANTERION. History Matching: A One Day Long Competition: Classical Approaches Versus Gradient Method. First international forum on reservoir simulation, Alpbach, Austria, 1998.    2. F. ANTERION, R. EYMARD and B. KARCHER. Use of Parameter Gradients for Reservoir History Matching. Symposium on Reservoir Simulation of the Society of Petroleum Engineers, Houston, Tex., 1989.    3. U. G. ARAKTINGI and W. M. BASHORE. Effects of Properties in Seismic Data on Reservoir Characterization and Consequent Fluid Flow Predictions When Integrated with Well Logs. SPE 24752, 67th Annual Technical Conference and Exhibition, Washington D.C., USA, 1992.    4. A. BAMBERGER, G. CHAVENT, and P. LAILLY. Une Application de La Théorie du Contrôle à un Problème Inverse de Sismique. Les annales de Géophysique Vol. 3, 1977.    5. R. BISSEL. Calculating Optimal Parameters for History Matching. 4th European Conference on the Mathematics of Oil Recovery, Roros, Norway, 1994.    6. R. BISSEL, J. E. KILLOUGH and Y. SHARMA. Reservoir History Matching Using the Method of Gradients on a Workstation. SPE 24265, Stavanger, Norway, 1992.    7. C. BOGAN, D. JOHNSON, M. LITVAK and D. STAUBER. Building Reservoir Models Based on 4D Seismic and Well Data in Gulf of Mexico Oil Fields. Annual Technical Conference and Exhibition, 2003.    8. J. BRAC, P. Y. DÉQUIREZ, F. NERVÉ, C. JACQUES, P. R. V. LAILLY and D. TRAN VAN HIEU. Inversion with a Priori Information: An Approach to Integrated Stratigraphic Interpretation. 58th Annual International SEG Meeting, Anaheim, Calif., 1988.    9. P. CARRION. Inverse Problems and Tomography in Acoustics and Seismology. Penn Publishing Company, 1987.    10. J. CÉA. Optimisation: Théories et Algorithmes. Dunod, 1971.    11. M. CHARARA, I. MAGNIANT, Y. MANIN, J.-P. DELHOMME and N. EBERLÉ. The Benefit of Coupling Geophysical Inversion Problems with Fluid Flow Simulation. ECMOR VII, Baveno, Lago Maggiore, Italy, 2000.    12. G. CHAVENT. Analyse Fonctionnelle et Identification des Coefficients Répartis Dans Les Équations Aux Dérivées Partielles. PhD Thesis, Université Paris VI, 1971.    13. G. CHAVENT. Identifiability of Parameters in Output Least Square Formulation. New York. 1987.    14. G. CHAVENT, M. DUPUY and P. LEMONNIER. History Matching by Use of Optimal Theory. SPE 4627, Las Vegas, Nev., 1973.    15. L. COSTA-REIS, G. DE MARSILY, and R. ESCHARD. Intégration de Données Dynamiques Dans un Modèle Géostatistique de Réservoir. PhD Thesis, Université Paris VI, 2000.    16. J.-E. DENNIS and R.-B. SCHNABEL. Numerical Methods for Unconstrained Optimization and Non-Linear Equation. Englewood Cliffs, N.J. 1983.    17. P. Y. DEQUIREZ and V. RICHARD. Application of Inversion to Integrated Stratigraphic Interpretation. Revue de l′Institut Français du pétrole, Vol. 45, no pp.-397, 416. 1990.    18. P. F. EDOA. Inversion de Formes Géologiques en Ingénierie De Gisements en en Utilisant les Données de Production. PhD Thesis, Université Paul Sabatier, 1999.    19. G. S. FEITOSA, L. CHU, L. G. THOMPSON and A. C. REYNOLDS. Determination of Permeability Distribution from Well Test Pressure Data. SPE 26047, 1993.    20. R. FLETCHER. Practical Methods of Optimization. New York. 1987.    21. F. GASSMAN N. Über die Elastiztät Poröser Medien. Vierteljahrresschr.Naturforschung Gesellschaft Vol. 96, pp. 1-23, Zurich, 1951.    22. O. GOSSELIN, A. COMINELLI, S. VAN DER BERG and S.-D. CHOWDHURY. A Gradient-Based Approach for History Matching of Both Production and 4D Seismic Data. ECMOR VII, Baveno, Lago Maggiore, Italy, 2000.    23. D. GUÉRILLOT and W. BEYDOUN. Reservoir Boundary Identification from Seismic Imaging for Well Test Analysis. SPE 26463, 68th Annual Technical Conference and Exhibition, Houston, Tex., USA, 1993.    24. L.-Y. HU. Gradual Deformation and Iterative Calibration of Gaussian-Related Stochastic Models. Mathematical Geology Vol. 32, pp. 87-108, 2000.    25. L.-Y. HU. Combinaison of Dependent Realizations within the Gradual Deformation Method. Mathematical Geology Vol. 34, pp. 953-963, 2002.    26. L.-Y. HU and G. BLANC. Constraining a Reservoir Facies Model to Dynamic Data Using a Gradual Deformation Method. 6th Conference on the Mathematics of Oil Recovery, Peebles, 1998.    27. P. JACQUARD and C. JAIN. Permeability Distribution from Field Pressure Data. SPE Journal pp. 281-294, 1965.    28. P. JACQUARD and C. JAIN. Recherche sur L'interprétation des Mesure de Pression. 2ème Colloque de l'ARTFP, Rueil-Malmaison, France, 1965.    29. J. W. JENNINGS, D. S. MC GREGOR and R. A. MORSE. Simultaneous Determination of Capillary Pressure and Relative Permeability by Automatic History Matching. SPE 14418, 1988.    30. A.-G. JOURNEL and DEUTSCH C.-V. Power Averaging for Block Effective Permeability. SPE Vol. 15128, 56th California Regional Meeting of the Society of Petroleum Engineers, Oakland. 1986.    31. V. KRETZ, M. LE RAVALEC-DUPIN and F. ROGGERO. An Integrated Reservoir Characterization Study Matching Production Data and 4D seismic. Annual Technical Conference and Exhibition, 2002.    32. G. KRUNETZ. Quelques Examples D'analyse D'enregistrements Sismiques. Geophysical Prospecting Vol. 11, pp. 409-422, 1963.    33. J. LANDA and R. HORNE. A Procedure to Integrate Well Test Data, Reservoir Performance History and 4D Seismic Information Into a Reservoir Description. SPE 38653, Annual Technical Conference and Exhibition, San Antonio, Tex., USA, 1997.    34. M. LAVERGNE. Méthodes Sismiques. Ecole Nationale Supérieure du Petrole et des Moteurs, Editions Technip, Paris. 1986.    35. M. LE RAVALEC, NOETINGER BENOÎT, and L.-Y. HU. The FFT Moving Average (FFT-MA) Generator: An Efficient Numerical Method for Generating and Conditioning Gaussian Simulation. Mathematical Geology Vol. 32, pp. 701-723, 2000.    36. M. LE RAVALEC-DUPIN and B. NOETINGER. Optimization with the Gradual Deformation Method. Mathematical Geology Vol. 34, No. 2, pp. 125-142, 1-2-2002.
37. J. L. LIONS. Contrôle Optimal de Systèmes Gouvernés Par des Équations aux Dérivées Partielles. Dunod, 1968.    38. F. MANSANNÉ. Algorithmes Génétiques: Applications à L'inversion Sismique et à L'extrapolation. PhD Thesis, UPPA, Pau, 2000.    39. M. MEZGHANI, A. FORNEL, V. LANGLAIS and N. LUCET. History Matching and Quantitative Use of 4D Seismic Data for an Improved Reservoir. SPE 90420, 2004.    40. M. MEZGHANI, A. FORNEL, V. LANGLAIS and N. LUCET. Quantitative Use of 4D Seismic Data For Geological Modeling & Reservoir Characterization Through History Matching. Paris, 2004.    41. M. MEZGHANI, F. ROGGERO and J. P. RAYMOND. Optimal Location of Pilot Points in History Matching. ECMOR VII, Baveno, Italy, 2000.    42. R. W. NELSON. In Place Measurement of Permeability in Heterogeneous Media; Theory of a Proposed Method. Geophys. Res. Vol. 66(5), pp. 2469-2478, 1960.    43. D. RAHON, G. BLANC and D. GUÉRILLOT. Gradient Method Constrained by Geological Bodies for History Matching. SPE 36568, 1996.    44. R. RAMAMOORTHY, W. F. MURPHY and C. COLL. Total Porosity Estimation in Shaly Sands From Shear Modulus. SPWLA 36th Annual Logging Symposium Transactions., 1995.    45. P. RENARD and G. DE MARSILY. Calculating Equivalent Permeability: A Review. Advances in Water Resources, Vol. 20, no 5-6, pp. 253-278, 1997.    46. F. ROGGERO and D. GUÉRILLOT. Gradient Method and Bayesian Formalism—Application to Petrophysical Parameter Characterization. 5th ECMOR, Leoben, Austria, 1996.    47. S. RONEN, C. ECONOMIDES and VARVIK. Synergetic Interpretation of Well Tests and Seismic Data for Reservoir Characterization. 54th EAEG Meeting, Paris, France, 1992.    48. B. H. RUSSEL. Introduction to Seismic Inversion Methods. SEG 1988.    49. A. TARANTOLA. Inverse Problem Theory: Method for Data Fitting and Model Parameter Estimation. Elseiver. 1987.    50. X. H. WEN and J. J. HERNANDEZ. Upscaling Hydraulic Conductivities in Heterogeneous Media: an Overview. Journal of Hydrology, Vol. 183, no pp. 9-32, 1996.    51. T. YAO and A.-G. JOURNEL. Porosity Modeling in a W. Texas Carbonate Reservoir Conditionned to Seismic Data: Solving the Difference of Scale Problem. SPE, Annual Technical Conference and Exhibition, 1998.    52. I. ZABALZA, G. BLANC, D. COLLOMBIER and M. MEZGHANI. Use of Experimental Design in Resolving Inverse Problems—Application to History Matching. ECMOR VII, Baveno, Italy, 2000.
To update geologic models, integration of the dynamic data is based on the inverse problem theory. Some parameters of the geologic model, such as porosity or permeability, are adjusted iteratively to fit observation data, such as production data for example. As in any inverse problem, there is not one and only solution. In order to reduce uncertainties on the production prediction, it is necessary to integrate more observation data (logs, production data, seismic data, . . . ), which allows to better constrain the models.